Long-term Behaviour of the Field in a Lossless Microscopic Maser

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Abstract
An asymptotic form of the density matrix for the field inside the cavity of a microscopic maser is derived. It is shown that it contains essentially the same information as that which has been inferred from numerical experiments in which the results of repeated measurements on the atoms as they leave the cavity have been taken into account. In particular, both approaches predict that the field, which is assumed to be initially of a thermal nature, evolves towards certain ‘trapping levels’. The analytic approach presented here is more general since it includes the evaluation of non-diagonal matrix elements.

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